"If in fact the American people can't trust that the border is controlled, you're never going to be able to pass this bill," declared Sen. Tom Coburn of Oklahoma, top Republican on the Senate Homeland Security and Governmental Affairs Committee.

His admonishment, joined by those of other GOP lawmakers, came as both Democratic and Republican senators filed a flurry of amendments ahead of the first votes Thursday in a separate committee on the far-reaching bill to deal with an estimated 11 million immigrants who are in the U.S. illegally and the millions more who might be expected to try to enter in the future. Some of the amendments could destroy the legislation's prospects by upending the carefully crafted deal negotiated over months by four Republican and four Democratic senators, supporters say.

Border security was the major sticking point on Tuesday.

"If we're going to get immigration reform through, if you're going to get it through the House, we're going to have to do a whole lot more on what is the definition of a controlled border than what is in this bill," said Coburn.

Sens. Rand Paul, R-Ky., and Ron Johnson, R-Wis., voiced similar concerns at a hearing to examine border security provisions of the bill. One of the legislation's authors, Sen. Marco Rubio, R-Fla., has already acknowledged that the bill will face a tough road to passage if those elements are not made stronger, and in a statement Tuesday he welcomed possible changes.

"In order for this bill to become law, it will have to be improved to bolster border security and enforcement even further and to limit the federal government's discretionary power in applying the law. In addition, additional measures will be required to address potential costs to taxpayers," Rubio said.

Later Tuesday, Rubio met privately with a large group of conservative activists to try to sell them on the bill, in part by offering assurances that their concerns could be addressed as the legislation moves forward. "I think it will move significantly to the right," Alex Nowrasteh, a policy analyst with the Cato Institute, said after emerging from the meeting.

Paul, a tea party favorite who has voiced support for comprehensive immigration overhaul, insisted his goal in raising questions about the bill is to make it better so it can pass not just the Democratic-controlled Senate but also the Republican-run House. He denied that he's out to kill the measure or slow it down.

"I want to be constructive in making the bill strong enough that conservatives, myself included, conservative Republicans in the House, will vote for this, because I think immigration reform is something we should do," Paul said.

"If it's not any stronger than this I don't see it getting through the House."

Echoing concerns raised by a number of Republicans, Paul said that the bill relies too much on setting goals and requiring studies about border security instead of insisting on actual accomplishments. Under the bill, "You have to have a plan to build a fence, but you don't have to build a fence," he complained.

Sen. Dick Durbin, D-Ill., an author of the legislation, defended the border security provisions and said that for some Republicans, border security is just their excuse to oppose immigration overhaul legislation.

Durbin said that border security is stronger than ever, but nonetheless "we went the extra step in this bill and they're saying it's still not enough. You kind of reach a point where you have to question their commitment to immigration reform."

The Homeland Security Department would have six months to create a new border-security plan to achieve the 90 percent effectiveness rate. Also within six months, the department would have to create a plan to identify where new fencing is needed. Once that happened, people who were in the U.S. illegally could begin to apply for a provisional legal status.

If the 90 percent rate wasn't achieved within five years, a commission made up of border state officials would make recommendations on how to do it.

After 10 years, people with provisional legal status could apply for permanent residency if the new security and fencing plans were operating, a new mandatory employment verification system was in place, and a new electronic exit system was tracking who leaves the country.

Among other things, Rubio has discussed strengthening the "triggers" that require certain steps to be taken before a path to citizenship can begin.

Officials with the Department of Homeland Security testified Tuesday that the U.S.-Mexico border is more secure than ever but they said the provisions in the bill would help them make it even stronger. They praised the pending legislation for directing more resources to the agency for surveillance equipment and for authorizing 3,500 new Border Patrol officers.

The hearing touched briefly on the Boston Marathon bombings, which exposed some failures, including an apparent lack of communication among federal agencies when one of the alleged bombers, Tamerlan Tsarnaev, traveled to Russia last year. A student from Kazakhstan accused of hiding evidence for one of the bombers also was allowed to return to the U.S. in January without a valid student visa.

Sen. John McCain, R-Ariz., an author of the immigration bill, said the legislation could be amended to address any such problems, particularly in the areas of humanitarian visas and student visas.